The present invention relates to a speech coding system with a speech encoder and a speech decoder cooperating with said speech encoder, the speech encoder comprising a pre-processor and an ADPCM (adaptive differential pulse code modulation) encoder with a quantizer and step-size adaptation means and the speech decoder comprising an ADPCM decoder with similar step-size adaptation means as in the ADPCM encoder and with a decoder, and a post-processor, the quantizer being provided with storage means containing values for a correction factor α((c(n)) of the step-size Δ(n), said correction factor being dependent on the quantizer output signal c(n).